Computational physics examples as IPython Notebooks.
The 4th order Runge-Kutta method was used to integrate the equations of motion for the system, then the pendulum was stabilised on its inverted equilibrium point using a proportional gain controller and linear quadratic regulator.
The trajectory of a charged particle propagating in a non-uniform magnetic field is calculated by solving the Lorentz force law using an embedded Runge-Kutta pair. The results show that the particle is mirrored.
An introduction to studying linear surface waves on an infinite domain. In particular, the problem of finding the time evolution of a small perturbation of the surface of an inviscid and incompressible fluid.
Self-avoiding random walks on the square lattice are performed using random sampling. The probability distribution of how many steps a random walker uses before it traps itself is studied. The notebook is based on an article by S. and P. C. Hemmer.
The Bak-Sneppen model of evolution is a simple model describing the evolution of an ecosystem. It offers a surprising amount of insight given its simplicity. This notebook does not deep dive into the model, but illustrates the basics using the Julia programming language.